Lesson plan
Bentley–Ottmann algorithm
In computational geometry, the Bentley–Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments, i.e. it finds the intersection points (or, simply, intersections) of line segments. It extends the Shamos–Hoey algorithm, a similar previous algorithm for testing whether or not a set of line segments has any crossings. For an input consisting of n line segments with k crossings (or intersections), the Bentley–Ottmann algorithm takes time \mathcal{O}((n + k) \log n) . In cases where k = \mathcal{o}\left(\frac{n^2}{\log n} \right) , this is an improvement on a naïve algorithm that tests every pair of segments, which takes \Theta(n^2) . The algorithm was initially developed by ; it is described in more detail in the textbooks , , and . Although asymptotically faster algorithms are now known by and , the Bentley–Ottmann algorithm remains a practical choice due to its simplicity and low memory requirements .
Article summary
In computational geometry, the Bentley–Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments, i.e. it finds the intersection points (or, simply, intersections) of line segments. It extends the Shamos–Hoey algorithm, a similar previous algorithm for testing whether or not a set of line segments has any crossings. For an input consisting of n line segments with k crossings (or intersections), the Bentley–Ottmann algorithm takes time \mathcal{O}((n + k) \log n) . In cases where k = \mathcal{o}\left(\frac{n^2}{\log n} \right) , this is an improvement on a naïve algorithm that tests every pair of segments, which takes \Theta(n^2) . The algorithm was initially developed by ; it is described in more detail in the textbooks , , and . Although asymptotically faster algorithms are now known by and , the Bentley–Ottmann algorithm remains a practical choice due to its simplicity and low memory requirements .
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.